A popular alternative to the boundary integral method is the level set method, which represents the interface implicitly as the zero level set of a higher dimensional hypersurface [1]}. A commonly cited advantage of the level set method is that it can easily handle complex interfacial behaviour such as the merging and splitting of interfaces. Another, more pertinent, advantage of the level set method is that it can describe the formation of complex interfacial patterns (such as those that occur in Hele–Shaw flow) on a uniform grid, eliminating the need to re-mesh as the interface evolves. One of the most significant drawbacks of the level set method is that it can suffer from mass loss/gain in regions where the mesh is under resolved. However, this issue can be mitigated by using the particle level set method [2]}, which uses massless marker particles to correct the location of the interface when mass is lost/gained. The level set method is a popular tool for studying moving boundary problems in fluid dynamics, and has been used to investigate interfacial instabilities that occur in Stefan problems [3]}, [4]} and Hele–Shaw flow [5]}, [6]}. We refer the reader to [7]}, [8]}, [9]} for more information about the level set method, including details regarding implementation and applications.
